On E−discretization of tori of compact simple Lie groups
Jiři ́ Patera · 2016
Abstract. The discrete orthogonality of special function families, called C- and S-functions, which are derived from the characters of compact simple Lie groups, is described in [3]. Here, the results of [3] are extended to two additional recently discovered families of special functions, called Ss − and Sl−functions. The main result is an explicit description of their pairwise discrete orthogonality within each family, when the functions are sampled on finite fragments F sM and F l M of a lattice in any dimension n ≥ 2 and of any density controlled by M, and of the symmetry of the weight lattice of any compact simple Lie group with two different lengths of roots.